On Tue, Oct 20, 2020 at 12:02 PM Jason Resch <[email protected]> wrote:
> On Monday, October 19, 2020, Bruce Kellett <[email protected]> wrote: > >> >> but the entropy at the bound increases only if the mass is also >> increased. >> >> When you say "at the bound" you are talking about black holes, which is > the point of maximum mass and maximum entropy for a given volume. > When you are far from the limit, as in most physical situations, the entropy bound is largely irrelevant. That is why I keep talking about black holes. It is only in that case, when the bound is saturated, that it is of any physical relevance. Most of your examples refer to physical situations that are far from saturating the bound. So in those case, talking about the bound is otiose. <snip> It's a generally accepted in computer science that a turing machine allowed >>> to use infinite space could store infinite information, even with fixed >>> total mass/energy. >>> >>> You do not have massless tapes on which to store your infinite >> information. So this would appear to be nonsensical. A Turing machine in a >> physical object, and it is subject to the laws of physics. >> > > The tape can be empty space, while the information can be represented by > placement of one particle in a definite location within that infinite space. > That does not make physical sense. How do you control the placement of your particle? How do you read its position? How do you know that it hasn't moved in the interim? Unless you have some physical way of fixing it in place, it conveys no useful information. Hence the need for a tape -- and you do not have access to massless tapes! <snip> That specifies the volume within which the energy is enclosed. But >> increasing the volume does not, of itself, increase the entropy. The >> maximum entropy for a fixed mass-energy is fixed by the surface area of a >> black hole of radius R = 2M. >> >> > That's false. The maximum entropy is NOT fixed unless both the > mass-energy AND the volume are fixed. > What do you think R = 2M does? If the bound were as you say, determined solely by mass-energy, then R > would not appear in the equation as it does. > At the limit, R is fixed by the mass. Putting a black hole in a bigger volume does not increase the entropy of >> that black hole. Specifying coordinates for the constituents of the BH is >> either irrelevant, or requires additional mass. >> > > See my grid example. No additional mass is needed for the black hole to > occupy a certain position in the grid. If the grid has is 10^10^100 cells, > then the location of the hole provides at least 10^100 bits of information. > This is more information/entropy than in even a galactic mass black hole. > See my discussion of the infinite tape. Similar considerations apply here. If you want to increase the entropy beyond what is given by the black hole, you have to increase the mass in the larger volume. Placing the BH arbitrarily in space does not increase the information, because it cannot encode any information unless its location is fixed in some physical manner. Bruce The upshot of all of this is that the expansion of space in a >> cosmology does not increase the maximum possible entropy. The maximum >> entropy is set by the amount of mass-energy in the cosmology, and that does >> not increase with the expansion. >> > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLSnXJpUo-dn2yfeS85FwY2oOvwkc-_J%2BGQ7YCG6t15HcQ%40mail.gmail.com.
